> NULL; > #`Assumptions:` #` 1 : All people in class were born in the US (For the sake of simplicity) Source: [https://www.behindthename.com/name/julian/top/united-states?type=sample] ` #` 2 : Assume all people in this class are between 18 and 30 years old (born from 1991-2003) for simplity [same source]` # #` 3 : Assume everyone has the same interest in math, regardless of name (For the sake of idealism) ` # #` 4: How to get the ratio ` #`Part 1: ` #`Taking the following sum:` #` Julians` :=(∑)(`pj__n`*`bb__n`)) #`Where (a): pj__n` represents "Percent Julian at YEAR n" #` (b): bb__n` represents "Babies born in the US at YEAR n" #`Part 2:` #`Taking the following sum:` # conjugate(J ) =(∑)(`bb__n`)-((∑)`pj__n`*`bb__n`)=Total babies - Total Julians #`Where bb__n` , again, represents "Babies born in the US at YEAR n" #We get the total number of People born in the US from 1991-2003 who are not named Julian, denoted as (J). #Part 3 : #We will start Create a recurrence, where: # We have n=18 steps, therefore we generate a sequence Sample:= Seq(J[][n] , n=1.. 18) which appends a #` Our first `conjugate(J[0])=J #`Part 4` #` #As there are 18 students in the classroom, we need to find K number of outcomes that have a total number of at least 2 Julians ` #`For ease of calculation, K is also equal to the total number of outcomes in which there are 1 Julian or 0 Julians, denoted as T`[0] and T[1] respectively. #`Let total probability =`(∑)(1-`T__n`/(Total people-n)) =(∑)(1-((conjugate(J)-n)!)/((Total people-n)!(Total people-n))) ; > ;